Problem Solving!


How To Solve It:

George Polya’s Four-Step Method:

  1. Understand the Problem

  2. Devise a Plan

  3. Carry Out the Plan

  4. Look Back


Bicycles and Tricycles

Jacinski’s Hardware has a number of bikes and tricycles for sell. There are 27 seats and 60 wheels all together. Determine how many bikes there are and how many tricycles there are. Please find your answer using at least two different Problem Solving Strategies.


Method 1: I understand that i have to find out how many bikes and tricycles there are.


Tricycle has 3 wheels. Bike has 2 wheels.

B+T=27        2B+3T=60

B=27-T         2(27-T)+3T=60

B+6=27        54-2T+T=60

B=21             54+T=60



Understand the Problem:

  • Break it into parts.

  • Do you have all the tools you need?

    • Enough information

    • Appropriate skills

  • Can you draw a picture?

    • Artistic skill not required

Devise a Plan:

  • Follow the clues systematically

  • Use rules of divisibility to limit possibilities, if possible

  • Use algebraic equations to find digits, if it applies

  • Draw to give yourself a visual whenever possible

  • We can do this mathematically using trial and error

  • We should be able to draw something to

Carry Out the Plan:

  • First, lets do it algebraically

  • We know there are 27 seats and 60 wheels

  • 27 seats tells us that is the max amount of bikes we could have

  • with that being said, we should be able to come up with a chart to help us out

Look Back:

  • What did i learn from this problem?

    • Review simple Algebra skills

    • Organized, local thinking


  • How can i use it to solve other problems?

  • Could i have used another method?

    • Trial and error, maybe (but why?)

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